The information that dreams happen only in REM is false in my experience. You can dream any moment.
In fact you are dreaming now, part of your mind is dreaming while your "ego" is focused on this physical experiment. Its all a matter of where your awareness is focused.

I know this will sound "esoteric" to many people because of bias and reading the same information everywhere but the more you expand your mind the better.
There is no harm in allowing yourself to believe that you can have lucid dreams at any time. REM means rapid eye mouvement and while there may be a technical reason for that to happen, there is dreams outside those episodes and for example when you do WILD they can be as realistic and vivid as rem dreams, in the same way that rem dreams can not be even noticed or remembered.